My son, Chuck, is a freshman in high school, and consequently, currently taking Algebra I. While Chuck has an excellent math mind, he occasionally struggles with the teaching method used in his class. He really likes his teacher, he just doesn't always get his explanations. His preferred method of dealing with this little instruction to comprehension glitch by contacting his sister's fiancé, Stephen, who has a Master's Degree in Chemistry and is a math whiz. Steve was a teacher at the University of California while he obtained his degree, so he's a great source and has credentials. When Steve explains things to him, Chuck gets it immediately. Chuck says that by the time that Steve is 2 sentences into his explanation of some algebraic equation he can begin to feel the fog burning off his brain and sunlight pouring through, illuminating the mysteries of math.
This is a phenomenon I have observed many times over the years in my own education and the education of my children. I have no idea why, but some math teachers, no matter how dedicated and well intentioned, just have difficulty imparting their understanding of math and numbers to others less gifted. Perhaps it is because many people with natural abilities in mathematics have trouble imagining what it is like to not get it. Perhaps it is a matter of style, presentation, or choice of wording...I don't know. I only know that it is very true.
I was an excellent student but I never had a powerful math mind. I had a good natural ability in geometry, which is spacial concepts, but algebra made my brain twitch. I have come to love math in my old age, but I had to work hard to get good grades in algebra. I had a friend of my older brother's tutor me and it worked just like Chuck and Stephen; when Howard explained math it was somehow yanked out of the murky primordial ooze and into the light of day. Unlike Chuck, it was instantaneously crystal clear for me, but I was willing to take what I could get.
When Chuck asked me the other day if I remembered Algebra I and polynomials all I could tell him was that it was so many years ago that I not only couldn't recall polynomials, I couldn't even remember Algebra I or my entire freshman year of high school. Chuck finds this amusing since I recall everything I ever learned about English grammar, can name all the Plantagenet Kings in order, describe the basic principals of black holes in space, and explain in great detail the Battle of Trafalgar, but he refrained from laughing at me about algebra, bless him.
I told him to call his go-to guy, Steve. He informed me that he had called him, but Steve was in the lab glued to an electron microscope looking at nanochemicals and was unavailable. Uh-oh... could be a math crisis coming on. I looked at the polynomials  the polynomials looked back at me. We decided that we had nothing in common and I went to call one of my former students, Mitch, who is an electrical and electronic engineering student at the University of Maine. I figured that any guy who could wire a particle accelerator had to know polynomials. He did, of course, and was able to impart the necessary knowledge to Chuck in about 5 minutes. Bless those who can do what I cannot.
I am willing to lend myself out as a test subject for all aspiring math teachers. In my plan they will be required to stand in front of me at a board and attempt to explain various algebraic equations to me. If I jump up from my chair and yell, “Eureka!”, they pass the test and can go teach. If I slump in my chair with a dazed look in my eyes and drool coming from my mouth, or start banging my head on the desk, they have to go back to school. I see this as a simple, but effective plan.
The problem is that people like Howard and Stephen, and Mitch, who have a gift for teaching math never seem to go on to teach it. I think that Howard became a history professor, Stephen plays with electron microscopes, and Mitch is probably going to build a super-computer. The math-challenged grieve for their loss. Now, of course, having established that I know zero about polynomials, and because I am a crazed lunatic, I am compelled to learn about them. No doubt about it  I have some issues.